I was reading a comment on MathOverflow and did not understand what was being suggested. I also don't understand Anton's response:
I initially thought Regenbogen's comment was being applied to the derivative of the dirac distribution, i.e. he wanted to extend this continuous linear functional from $D$ to $C$. But I don't understand what dominating semi-norm (sublinear functional) he had in mind... And I don't understand Anton's response - How are the derivatives of the delta distribution not bounded linear functionals on $D$? They seem to have operator norm equal to 1.
Then I thought perhaps he literally was referring to the measure mentioned earlier, i.e. a Radon measure acting as a distribution on $C$ and trivially extending to $D$... but this also seems to be a bounded linear functional on both $C$ and $D$.
Can someone explain what was being suggested, and how Anton's response makes sense?